1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 383,201 x 11
##    site_type date       sex   age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr> <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 fema… miss… e380000… nhs_glo…     1 gl34fe   South West
##  2 111       2020-03-18 fema… miss… e380001… nhs_sou…     1 ne325nn  North Eas…
##  3 111       2020-03-18 fema… 0-18  e380000… nhs_air…     8 bd57jr   North Eas…
##  4 111       2020-03-18 fema… 0-18  e380000… nhs_ash…     7 tn254ab  South East
##  5 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  6 111       2020-03-18 fema… 0-18  e380000… nhs_bar…     9 n111np   London    
##  7 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    11 s752py   North Eas…
##  8 111       2020-03-18 fema… 0-18  e380000… nhs_bas…    19 ss143hg  East of E…
##  9 111       2020-03-18 fema… 0-18  e380000… nhs_bas…     6 dn227xf  North Eas…
## 10 111       2020-03-18 fema… 0-18  e380000… nhs_bat…     9 ba25rp   South West
## # … with 383,191 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##      date_report               nhs_region deaths
## 1     2020-03-01          East of England      0
## 2     2020-03-02          East of England      1
## 3     2020-03-03          East of England      0
## 4     2020-03-04          East of England      0
## 5     2020-03-05          East of England      0
## 6     2020-03-06          East of England      1
## 7     2020-03-07          East of England      0
## 8     2020-03-08          East of England      0
## 9     2020-03-09          East of England      1
## 10    2020-03-10          East of England      0
## 11    2020-03-11          East of England      0
## 12    2020-03-12          East of England      0
## 13    2020-03-13          East of England      1
## 14    2020-03-14          East of England      2
## 15    2020-03-15          East of England      2
## 16    2020-03-16          East of England      1
## 17    2020-03-17          East of England      1
## 18    2020-03-18          East of England      5
## 19    2020-03-19          East of England      4
## 20    2020-03-20          East of England      2
## 21    2020-03-21          East of England     11
## 22    2020-03-22          East of England     12
## 23    2020-03-23          East of England     11
## 24    2020-03-24          East of England     19
## 25    2020-03-25          East of England     26
## 26    2020-03-26          East of England     36
## 27    2020-03-27          East of England     38
## 28    2020-03-28          East of England     28
## 29    2020-03-29          East of England     43
## 30    2020-03-30          East of England     45
## 31    2020-03-31          East of England     70
## 32    2020-04-01          East of England     62
## 33    2020-04-02          East of England     65
## 34    2020-04-03          East of England     80
## 35    2020-04-04          East of England     71
## 36    2020-04-05          East of England     76
## 37    2020-04-06          East of England     71
## 38    2020-04-07          East of England     93
## 39    2020-04-08          East of England    111
## 40    2020-04-09          East of England     87
## 41    2020-04-10          East of England     74
## 42    2020-04-11          East of England     92
## 43    2020-04-12          East of England    100
## 44    2020-04-13          East of England     78
## 45    2020-04-14          East of England     61
## 46    2020-04-15          East of England     82
## 47    2020-04-16          East of England     74
## 48    2020-04-17          East of England     86
## 49    2020-04-18          East of England     64
## 50    2020-04-19          East of England     67
## 51    2020-04-20          East of England     67
## 52    2020-04-21          East of England     75
## 53    2020-04-22          East of England     67
## 54    2020-04-23          East of England     49
## 55    2020-04-24          East of England     66
## 56    2020-04-25          East of England     54
## 57    2020-04-26          East of England     48
## 58    2020-04-27          East of England     46
## 59    2020-04-28          East of England     58
## 60    2020-04-29          East of England     32
## 61    2020-04-30          East of England     45
## 62    2020-05-01          East of England     49
## 63    2020-05-02          East of England     29
## 64    2020-05-03          East of England     41
## 65    2020-05-04          East of England     19
## 66    2020-05-05          East of England     36
## 67    2020-05-06          East of England     31
## 68    2020-05-07          East of England     33
## 69    2020-05-08          East of England     33
## 70    2020-05-09          East of England     29
## 71    2020-05-10          East of England     22
## 72    2020-05-11          East of England     18
## 73    2020-05-12          East of England     21
## 74    2020-05-13          East of England     27
## 75    2020-05-14          East of England     26
## 76    2020-05-15          East of England     19
## 77    2020-05-16          East of England     26
## 78    2020-05-17          East of England     17
## 79    2020-05-18          East of England     25
## 80    2020-05-19          East of England     15
## 81    2020-05-20          East of England     26
## 82    2020-05-21          East of England     21
## 83    2020-05-22          East of England     13
## 84    2020-05-23          East of England     12
## 85    2020-05-24          East of England     17
## 86    2020-05-25          East of England     25
## 87    2020-05-26          East of England     14
## 88    2020-05-27          East of England     12
## 89    2020-05-28          East of England     17
## 90    2020-05-29          East of England     16
## 91    2020-05-30          East of England      9
## 92    2020-05-31          East of England      8
## 93    2020-06-01          East of England     17
## 94    2020-06-02          East of England     14
## 95    2020-06-03          East of England     10
## 96    2020-06-04          East of England      7
## 97    2020-06-05          East of England     14
## 98    2020-06-06          East of England      5
## 99    2020-06-07          East of England      9
## 100   2020-06-08          East of England      7
## 101   2020-06-09          East of England      6
## 102   2020-06-10          East of England      8
## 103   2020-06-11          East of England      1
## 104   2020-06-12          East of England      9
## 105   2020-06-13          East of England      5
## 106   2020-06-14          East of England      4
## 107   2020-06-15          East of England      8
## 108   2020-06-16          East of England      3
## 109   2020-06-17          East of England      7
## 110   2020-06-18          East of England      4
## 111   2020-06-19          East of England      7
## 112   2020-06-20          East of England      4
## 113   2020-06-21          East of England      3
## 114   2020-06-22          East of England      6
## 115   2020-06-23          East of England      5
## 116   2020-06-24          East of England      4
## 117   2020-06-25          East of England      1
## 118   2020-06-26          East of England      5
## 119   2020-06-27          East of England      6
## 120   2020-06-28          East of England      8
## 121   2020-06-29          East of England      4
## 122   2020-06-30          East of England      5
## 123   2020-07-01          East of England      2
## 124   2020-07-02          East of England      5
## 125   2020-07-03          East of England      0
## 126   2020-07-04          East of England      3
## 127   2020-07-05          East of England      1
## 128   2020-07-06          East of England      2
## 129   2020-07-07          East of England      2
## 130   2020-07-08          East of England      0
## 131   2020-07-09          East of England      8
## 132   2020-07-10          East of England      4
## 133   2020-07-11          East of England      2
## 134   2020-07-12          East of England      1
## 135   2020-07-13          East of England      8
## 136   2020-07-14          East of England      2
## 137   2020-07-15          East of England      0
## 138   2020-07-16          East of England      0
## 139   2020-07-17          East of England      0
## 140   2020-07-18          East of England      0
## 141   2020-07-19          East of England      1
## 142   2020-07-20          East of England      1
## 143   2020-07-21          East of England      1
## 144   2020-07-22          East of England      2
## 145   2020-07-23          East of England      1
## 146   2020-07-24          East of England      1
## 147   2020-07-25          East of England      0
## 148   2020-07-26          East of England      1
## 149   2020-07-27          East of England      1
## 150   2020-07-28          East of England      2
## 151   2020-07-29          East of England      0
## 152   2020-07-30          East of England      0
## 153   2020-07-31          East of England      1
## 154   2020-08-01          East of England      0
## 155   2020-08-02          East of England      0
## 156   2020-08-03          East of England      0
## 157   2020-08-04          East of England      1
## 158   2020-08-05          East of England      1
## 159   2020-08-06          East of England      0
## 160   2020-08-07          East of England      1
## 161   2020-08-08          East of England      0
## 162   2020-08-09          East of England      0
## 163   2020-08-10          East of England      1
## 164   2020-08-11          East of England      2
## 165   2020-08-12          East of England      1
## 166   2020-08-13          East of England      0
## 167   2020-08-14          East of England      1
## 168   2020-08-15          East of England      1
## 169   2020-08-16          East of England      0
## 170   2020-08-17          East of England      0
## 171   2020-08-18          East of England      2
## 172   2020-08-19          East of England      1
## 173   2020-08-20          East of England      1
## 174   2020-08-21          East of England      0
## 175   2020-08-22          East of England      1
## 176   2020-08-23          East of England      1
## 177   2020-08-24          East of England      0
## 178   2020-08-25          East of England      0
## 179   2020-08-26          East of England      1
## 180   2020-08-27          East of England      1
## 181   2020-08-28          East of England      0
## 182   2020-08-29          East of England      0
## 183   2020-08-30          East of England      0
## 184   2020-08-31          East of England      0
## 185   2020-09-01          East of England      0
## 186   2020-09-02          East of England      0
## 187   2020-09-03          East of England      1
## 188   2020-09-04          East of England      1
## 189   2020-09-05          East of England      0
## 190   2020-09-06          East of England      1
## 191   2020-09-07          East of England      0
## 192   2020-09-08          East of England      0
## 193   2020-09-09          East of England      0
## 194   2020-09-10          East of England      0
## 195   2020-09-11          East of England      0
## 196   2020-09-12          East of England      0
## 197   2020-09-13          East of England      1
## 198   2020-09-14          East of England      1
## 199   2020-09-15          East of England      0
## 200   2020-09-16          East of England      0
## 201   2020-09-17          East of England      0
## 202   2020-09-18          East of England      0
## 203   2020-09-19          East of England      0
## 204   2020-09-20          East of England      2
## 205   2020-09-21          East of England      0
## 206   2020-09-22          East of England      2
## 207   2020-09-23          East of England      1
## 208   2020-09-24          East of England      0
## 209   2020-09-25          East of England      1
## 210   2020-09-26          East of England      1
## 211   2020-09-27          East of England      1
## 212   2020-09-28          East of England      2
## 213   2020-09-29          East of England      2
## 214   2020-09-30          East of England      2
## 215   2020-10-01          East of England      2
## 216   2020-10-02          East of England      1
## 217   2020-10-03          East of England      1
## 218   2020-10-04          East of England      0
## 219   2020-10-05          East of England      0
## 220   2020-10-06          East of England      4
## 221   2020-10-07          East of England      6
## 222   2020-10-08          East of England      3
## 223   2020-10-09          East of England      1
## 224   2020-10-10          East of England      6
## 225   2020-10-11          East of England      2
## 226   2020-10-12          East of England      2
## 227   2020-10-13          East of England      1
## 228   2020-10-14          East of England      3
## 229   2020-10-15          East of England      4
## 230   2020-10-16          East of England      5
## 231   2020-10-17          East of England      6
## 232   2020-10-18          East of England      7
## 233   2020-10-19          East of England      5
## 234   2020-10-20          East of England      9
## 235   2020-10-21          East of England      7
## 236   2020-10-22          East of England      7
## 237   2020-10-23          East of England     14
## 238   2020-10-24          East of England      1
## 239   2020-10-25          East of England     10
## 240   2020-10-26          East of England     10
## 241   2020-10-27          East of England      8
## 242   2020-10-28          East of England     12
## 243   2020-10-29          East of England     10
## 244   2020-10-30          East of England     12
## 245   2020-10-31          East of England     15
## 246   2020-11-01          East of England     14
## 247   2020-11-02          East of England      9
## 248   2020-11-03          East of England     14
## 249   2020-11-04          East of England     11
## 250   2020-11-05          East of England     10
## 251   2020-11-06          East of England     18
## 252   2020-11-07          East of England     10
## 253   2020-11-08          East of England     13
## 254   2020-11-09          East of England     15
## 255   2020-11-10          East of England     26
## 256   2020-11-11          East of England     14
## 257   2020-11-12          East of England     14
## 258   2020-11-13          East of England     21
## 259   2020-11-14          East of England     19
## 260   2020-11-15          East of England     13
## 261   2020-11-16          East of England     11
## 262   2020-11-17          East of England     17
## 263   2020-11-18          East of England     19
## 264   2020-11-19          East of England     23
## 265   2020-11-20          East of England     24
## 266   2020-11-21          East of England     19
## 267   2020-11-22          East of England     21
## 268   2020-11-23          East of England     18
## 269   2020-11-24          East of England     21
## 270   2020-11-25          East of England     19
## 271   2020-11-26          East of England     19
## 272   2020-11-27          East of England     14
## 273   2020-11-28          East of England     28
## 274   2020-11-29          East of England     19
## 275   2020-11-30          East of England     22
## 276   2020-12-01          East of England     24
## 277   2020-12-02          East of England     18
## 278   2020-12-03          East of England     23
## 279   2020-12-04          East of England     24
## 280   2020-12-05          East of England     22
## 281   2020-12-06          East of England     19
## 282   2020-12-07          East of England     16
## 283   2020-12-08          East of England     24
## 284   2020-12-09          East of England     19
## 285   2020-12-10          East of England     31
## 286   2020-12-11          East of England     30
## 287   2020-12-12          East of England     24
## 288   2020-12-13          East of England     23
## 289   2020-12-14          East of England     26
## 290   2020-12-15          East of England     31
## 291   2020-12-16          East of England     26
## 292   2020-12-17          East of England     34
## 293   2020-12-18          East of England     35
## 294   2020-12-19          East of England     42
## 295   2020-12-20          East of England     44
## 296   2020-12-21          East of England     55
## 297   2020-12-22          East of England     42
## 298   2020-12-23          East of England     46
## 299   2020-12-24          East of England     39
## 300   2020-12-25          East of England     46
## 301   2020-12-26          East of England     47
## 302   2020-12-27          East of England     37
## 303   2020-12-28          East of England     49
## 304   2020-12-29          East of England     34
## 305   2020-12-30          East of England     38
## 306   2020-12-31          East of England      2
## 307   2020-03-01                   London      0
## 308   2020-03-02                   London      0
## 309   2020-03-03                   London      0
## 310   2020-03-04                   London      0
## 311   2020-03-05                   London      0
## 312   2020-03-06                   London      1
## 313   2020-03-07                   London      0
## 314   2020-03-08                   London      0
## 315   2020-03-09                   London      1
## 316   2020-03-10                   London      0
## 317   2020-03-11                   London      5
## 318   2020-03-12                   London      6
## 319   2020-03-13                   London     10
## 320   2020-03-14                   London     13
## 321   2020-03-15                   London      9
## 322   2020-03-16                   London     15
## 323   2020-03-17                   London     23
## 324   2020-03-18                   London     28
## 325   2020-03-19                   London     25
## 326   2020-03-20                   London     44
## 327   2020-03-21                   London     49
## 328   2020-03-22                   London     54
## 329   2020-03-23                   London     63
## 330   2020-03-24                   London     86
## 331   2020-03-25                   London    112
## 332   2020-03-26                   London    130
## 333   2020-03-27                   London    130
## 334   2020-03-28                   London    123
## 335   2020-03-29                   London    145
## 336   2020-03-30                   London    151
## 337   2020-03-31                   London    183
## 338   2020-04-01                   London    202
## 339   2020-04-02                   London    191
## 340   2020-04-03                   London    199
## 341   2020-04-04                   London    231
## 342   2020-04-05                   London    195
## 343   2020-04-06                   London    198
## 344   2020-04-07                   London    220
## 345   2020-04-08                   London    239
## 346   2020-04-09                   London    207
## 347   2020-04-10                   London    171
## 348   2020-04-11                   London    178
## 349   2020-04-12                   London    159
## 350   2020-04-13                   London    166
## 351   2020-04-14                   London    143
## 352   2020-04-15                   London    143
## 353   2020-04-16                   London    140
## 354   2020-04-17                   London    101
## 355   2020-04-18                   London    101
## 356   2020-04-19                   London    103
## 357   2020-04-20                   London     96
## 358   2020-04-21                   London     96
## 359   2020-04-22                   London    109
## 360   2020-04-23                   London     77
## 361   2020-04-24                   London     71
## 362   2020-04-25                   London     58
## 363   2020-04-26                   London     53
## 364   2020-04-27                   London     52
## 365   2020-04-28                   London     44
## 366   2020-04-29                   London     45
## 367   2020-04-30                   London     40
## 368   2020-05-01                   London     41
## 369   2020-05-02                   London     41
## 370   2020-05-03                   London     36
## 371   2020-05-04                   London     30
## 372   2020-05-05                   London     25
## 373   2020-05-06                   London     37
## 374   2020-05-07                   London     37
## 375   2020-05-08                   London     30
## 376   2020-05-09                   London     23
## 377   2020-05-10                   London     26
## 378   2020-05-11                   London     18
## 379   2020-05-12                   London     18
## 380   2020-05-13                   London     17
## 381   2020-05-14                   London     20
## 382   2020-05-15                   London     19
## 383   2020-05-16                   London     14
## 384   2020-05-17                   London     15
## 385   2020-05-18                   London     11
## 386   2020-05-19                   London     14
## 387   2020-05-20                   London     19
## 388   2020-05-21                   London     12
## 389   2020-05-22                   London     10
## 390   2020-05-23                   London      6
## 391   2020-05-24                   London      7
## 392   2020-05-25                   London      9
## 393   2020-05-26                   London     14
## 394   2020-05-27                   London      7
## 395   2020-05-28                   London      8
## 396   2020-05-29                   London      7
## 397   2020-05-30                   London     12
## 398   2020-05-31                   London      6
## 399   2020-06-01                   London     10
## 400   2020-06-02                   London      8
## 401   2020-06-03                   London      6
## 402   2020-06-04                   London      8
## 403   2020-06-05                   London      4
## 404   2020-06-06                   London      0
## 405   2020-06-07                   London      5
## 406   2020-06-08                   London      5
## 407   2020-06-09                   London      5
## 408   2020-06-10                   London      8
## 409   2020-06-11                   London      5
## 410   2020-06-12                   London      3
## 411   2020-06-13                   London      3
## 412   2020-06-14                   London      3
## 413   2020-06-15                   London      1
## 414   2020-06-16                   London      2
## 415   2020-06-17                   London      1
## 416   2020-06-18                   London      2
## 417   2020-06-19                   London      5
## 418   2020-06-20                   London      3
## 419   2020-06-21                   London      4
## 420   2020-06-22                   London      2
## 421   2020-06-23                   London      1
## 422   2020-06-24                   London      4
## 423   2020-06-25                   London      3
## 424   2020-06-26                   London      2
## 425   2020-06-27                   London      1
## 426   2020-06-28                   London      2
## 427   2020-06-29                   London      2
## 428   2020-06-30                   London      1
## 429   2020-07-01                   London      3
## 430   2020-07-02                   London      2
## 431   2020-07-03                   London      2
## 432   2020-07-04                   London      1
## 433   2020-07-05                   London      3
## 434   2020-07-06                   London      2
## 435   2020-07-07                   London      1
## 436   2020-07-08                   London      3
## 437   2020-07-09                   London      4
## 438   2020-07-10                   London      0
## 439   2020-07-11                   London      1
## 440   2020-07-12                   London      1
## 441   2020-07-13                   London      1
## 442   2020-07-14                   London      0
## 443   2020-07-15                   London      2
## 444   2020-07-16                   London      0
## 445   2020-07-17                   London      0
## 446   2020-07-18                   London      2
## 447   2020-07-19                   London      0
## 448   2020-07-20                   London      0
## 449   2020-07-21                   London      1
## 450   2020-07-22                   London      0
## 451   2020-07-23                   London      2
## 452   2020-07-24                   London      0
## 453   2020-07-25                   London      1
## 454   2020-07-26                   London      0
## 455   2020-07-27                   London      1
## 456   2020-07-28                   London      0
## 457   2020-07-29                   London      0
## 458   2020-07-30                   London      1
## 459   2020-07-31                   London      0
## 460   2020-08-01                   London      0
## 461   2020-08-02                   London      3
## 462   2020-08-03                   London      0
## 463   2020-08-04                   London      0
## 464   2020-08-05                   London      0
## 465   2020-08-06                   London      1
## 466   2020-08-07                   London      0
## 467   2020-08-08                   London      0
## 468   2020-08-09                   London      0
## 469   2020-08-10                   London      0
## 470   2020-08-11                   London      1
## 471   2020-08-12                   London      0
## 472   2020-08-13                   London      2
## 473   2020-08-14                   London      0
## 474   2020-08-15                   London      0
## 475   2020-08-16                   London      0
## 476   2020-08-17                   London      1
## 477   2020-08-18                   London      1
## 478   2020-08-19                   London      0
## 479   2020-08-20                   London      1
## 480   2020-08-21                   London      0
## 481   2020-08-22                   London      0
## 482   2020-08-23                   London      0
## 483   2020-08-24                   London      1
## 484   2020-08-25                   London      1
## 485   2020-08-26                   London      0
## 486   2020-08-27                   London      0
## 487   2020-08-28                   London      0
## 488   2020-08-29                   London      0
## 489   2020-08-30                   London      0
## 490   2020-08-31                   London      1
## 491   2020-09-01                   London      0
## 492   2020-09-02                   London      1
## 493   2020-09-03                   London      1
## 494   2020-09-04                   London      0
## 495   2020-09-05                   London      0
## 496   2020-09-06                   London      2
## 497   2020-09-07                   London      0
## 498   2020-09-08                   London      0
## 499   2020-09-09                   London      0
## 500   2020-09-10                   London      2
## 501   2020-09-11                   London      1
## 502   2020-09-12                   London      1
## 503   2020-09-13                   London      0
## 504   2020-09-14                   London      0
## 505   2020-09-15                   London      1
## 506   2020-09-16                   London      2
## 507   2020-09-17                   London      2
## 508   2020-09-18                   London      1
## 509   2020-09-19                   London      3
## 510   2020-09-20                   London      3
## 511   2020-09-21                   London      2
## 512   2020-09-22                   London      6
## 513   2020-09-23                   London      4
## 514   2020-09-24                   London      3
## 515   2020-09-25                   London      1
## 516   2020-09-26                   London      1
## 517   2020-09-27                   London      1
## 518   2020-09-28                   London      3
## 519   2020-09-29                   London      7
## 520   2020-09-30                   London      6
## 521   2020-10-01                   London      4
## 522   2020-10-02                   London      1
## 523   2020-10-03                   London      3
## 524   2020-10-04                   London      2
## 525   2020-10-05                   London      7
## 526   2020-10-06                   London      4
## 527   2020-10-07                   London      6
## 528   2020-10-08                   London      6
## 529   2020-10-09                   London      7
## 530   2020-10-10                   London      3
## 531   2020-10-11                   London      5
## 532   2020-10-12                   London      7
## 533   2020-10-13                   London      4
## 534   2020-10-14                   London      6
## 535   2020-10-15                   London     13
## 536   2020-10-16                   London      6
## 537   2020-10-17                   London      2
## 538   2020-10-18                   London      5
## 539   2020-10-19                   London     11
## 540   2020-10-20                   London      8
## 541   2020-10-21                   London     14
## 542   2020-10-22                   London     12
## 543   2020-10-23                   London      7
## 544   2020-10-24                   London     18
## 545   2020-10-25                   London     10
## 546   2020-10-26                   London     10
## 547   2020-10-27                   London     12
## 548   2020-10-28                   London     23
## 549   2020-10-29                   London     14
## 550   2020-10-30                   London     17
## 551   2020-10-31                   London      7
## 552   2020-11-01                   London     17
## 553   2020-11-02                   London     16
## 554   2020-11-03                   London     10
## 555   2020-11-04                   London     18
## 556   2020-11-05                   London     17
## 557   2020-11-06                   London     12
## 558   2020-11-07                   London     21
## 559   2020-11-08                   London     15
## 560   2020-11-09                   London     28
## 561   2020-11-10                   London     14
## 562   2020-11-11                   London     14
## 563   2020-11-12                   London     15
## 564   2020-11-13                   London     14
## 565   2020-11-14                   London     20
## 566   2020-11-15                   London     18
## 567   2020-11-16                   London     29
## 568   2020-11-17                   London     29
## 569   2020-11-18                   London     22
## 570   2020-11-19                   London     24
## 571   2020-11-20                   London     19
## 572   2020-11-21                   London     18
## 573   2020-11-22                   London     26
## 574   2020-11-23                   London     19
## 575   2020-11-24                   London     26
## 576   2020-11-25                   London     30
## 577   2020-11-26                   London     25
## 578   2020-11-27                   London     28
## 579   2020-11-28                   London     23
## 580   2020-11-29                   London     40
## 581   2020-11-30                   London     19
## 582   2020-12-01                   London     28
## 583   2020-12-02                   London     28
## 584   2020-12-03                   London     27
## 585   2020-12-04                   London     29
## 586   2020-12-05                   London     23
## 587   2020-12-06                   London     24
## 588   2020-12-07                   London     29
## 589   2020-12-08                   London     35
## 590   2020-12-09                   London     27
## 591   2020-12-10                   London     28
## 592   2020-12-11                   London     26
## 593   2020-12-12                   London     33
## 594   2020-12-13                   London     33
## 595   2020-12-14                   London     37
## 596   2020-12-15                   London     49
## 597   2020-12-16                   London     35
## 598   2020-12-17                   London     55
## 599   2020-12-18                   London     40
## 600   2020-12-19                   London     38
## 601   2020-12-20                   London     50
## 602   2020-12-21                   London     55
## 603   2020-12-22                   London     52
## 604   2020-12-23                   London     54
## 605   2020-12-24                   London     55
## 606   2020-12-25                   London     67
## 607   2020-12-26                   London     70
## 608   2020-12-27                   London     75
## 609   2020-12-28                   London     64
## 610   2020-12-29                   London     70
## 611   2020-12-30                   London     38
## 612   2020-12-31                   London      6
## 613   2020-03-01                 Midlands      0
## 614   2020-03-02                 Midlands      0
## 615   2020-03-03                 Midlands      1
## 616   2020-03-04                 Midlands      0
## 617   2020-03-05                 Midlands      0
## 618   2020-03-06                 Midlands      0
## 619   2020-03-07                 Midlands      0
## 620   2020-03-08                 Midlands      2
## 621   2020-03-09                 Midlands      1
## 622   2020-03-10                 Midlands      0
## 623   2020-03-11                 Midlands      2
## 624   2020-03-12                 Midlands      6
## 625   2020-03-13                 Midlands      5
## 626   2020-03-14                 Midlands      4
## 627   2020-03-15                 Midlands      5
## 628   2020-03-16                 Midlands     11
## 629   2020-03-17                 Midlands      8
## 630   2020-03-18                 Midlands     13
## 631   2020-03-19                 Midlands      8
## 632   2020-03-20                 Midlands     28
## 633   2020-03-21                 Midlands     13
## 634   2020-03-22                 Midlands     31
## 635   2020-03-23                 Midlands     33
## 636   2020-03-24                 Midlands     41
## 637   2020-03-25                 Midlands     48
## 638   2020-03-26                 Midlands     64
## 639   2020-03-27                 Midlands     72
## 640   2020-03-28                 Midlands     89
## 641   2020-03-29                 Midlands     92
## 642   2020-03-30                 Midlands     90
## 643   2020-03-31                 Midlands    123
## 644   2020-04-01                 Midlands    140
## 645   2020-04-02                 Midlands    142
## 646   2020-04-03                 Midlands    124
## 647   2020-04-04                 Midlands    151
## 648   2020-04-05                 Midlands    164
## 649   2020-04-06                 Midlands    140
## 650   2020-04-07                 Midlands    123
## 651   2020-04-08                 Midlands    186
## 652   2020-04-09                 Midlands    140
## 653   2020-04-10                 Midlands    127
## 654   2020-04-11                 Midlands    142
## 655   2020-04-12                 Midlands    139
## 656   2020-04-13                 Midlands    120
## 657   2020-04-14                 Midlands    116
## 658   2020-04-15                 Midlands    147
## 659   2020-04-16                 Midlands    102
## 660   2020-04-17                 Midlands    118
## 661   2020-04-18                 Midlands    115
## 662   2020-04-19                 Midlands     93
## 663   2020-04-20                 Midlands    107
## 664   2020-04-21                 Midlands     86
## 665   2020-04-22                 Midlands     78
## 666   2020-04-23                 Midlands    103
## 667   2020-04-24                 Midlands     79
## 668   2020-04-25                 Midlands     72
## 669   2020-04-26                 Midlands     81
## 670   2020-04-27                 Midlands     74
## 671   2020-04-28                 Midlands     68
## 672   2020-04-29                 Midlands     53
## 673   2020-04-30                 Midlands     56
## 674   2020-05-01                 Midlands     64
## 675   2020-05-02                 Midlands     51
## 676   2020-05-03                 Midlands     52
## 677   2020-05-04                 Midlands     61
## 678   2020-05-05                 Midlands     59
## 679   2020-05-06                 Midlands     59
## 680   2020-05-07                 Midlands     48
## 681   2020-05-08                 Midlands     34
## 682   2020-05-09                 Midlands     37
## 683   2020-05-10                 Midlands     42
## 684   2020-05-11                 Midlands     33
## 685   2020-05-12                 Midlands     45
## 686   2020-05-13                 Midlands     40
## 687   2020-05-14                 Midlands     39
## 688   2020-05-15                 Midlands     40
## 689   2020-05-16                 Midlands     34
## 690   2020-05-17                 Midlands     31
## 691   2020-05-18                 Midlands     36
## 692   2020-05-19                 Midlands     35
## 693   2020-05-20                 Midlands     36
## 694   2020-05-21                 Midlands     32
## 695   2020-05-22                 Midlands     27
## 696   2020-05-23                 Midlands     34
## 697   2020-05-24                 Midlands     20
## 698   2020-05-25                 Midlands     26
## 699   2020-05-26                 Midlands     33
## 700   2020-05-27                 Midlands     29
## 701   2020-05-28                 Midlands     28
## 702   2020-05-29                 Midlands     20
## 703   2020-05-30                 Midlands     21
## 704   2020-05-31                 Midlands     22
## 705   2020-06-01                 Midlands     20
## 706   2020-06-02                 Midlands     22
## 707   2020-06-03                 Midlands     24
## 708   2020-06-04                 Midlands     16
## 709   2020-06-05                 Midlands     21
## 710   2020-06-06                 Midlands     20
## 711   2020-06-07                 Midlands     17
## 712   2020-06-08                 Midlands     16
## 713   2020-06-09                 Midlands     18
## 714   2020-06-10                 Midlands     15
## 715   2020-06-11                 Midlands     13
## 716   2020-06-12                 Midlands     12
## 717   2020-06-13                 Midlands      6
## 718   2020-06-14                 Midlands     18
## 719   2020-06-15                 Midlands     12
## 720   2020-06-16                 Midlands     15
## 721   2020-06-17                 Midlands     11
## 722   2020-06-18                 Midlands     15
## 723   2020-06-19                 Midlands     10
## 724   2020-06-20                 Midlands     15
## 725   2020-06-21                 Midlands     14
## 726   2020-06-22                 Midlands     14
## 727   2020-06-23                 Midlands     16
## 728   2020-06-24                 Midlands     15
## 729   2020-06-25                 Midlands     18
## 730   2020-06-26                 Midlands      5
## 731   2020-06-27                 Midlands      5
## 732   2020-06-28                 Midlands      7
## 733   2020-06-29                 Midlands      6
## 734   2020-06-30                 Midlands      6
## 735   2020-07-01                 Midlands      7
## 736   2020-07-02                 Midlands     10
## 737   2020-07-03                 Midlands      3
## 738   2020-07-04                 Midlands      4
## 739   2020-07-05                 Midlands      6
## 740   2020-07-06                 Midlands      5
## 741   2020-07-07                 Midlands      3
## 742   2020-07-08                 Midlands      5
## 743   2020-07-09                 Midlands      9
## 744   2020-07-10                 Midlands      3
## 745   2020-07-11                 Midlands      0
## 746   2020-07-12                 Midlands      5
## 747   2020-07-13                 Midlands      1
## 748   2020-07-14                 Midlands      1
## 749   2020-07-15                 Midlands      6
## 750   2020-07-16                 Midlands      2
## 751   2020-07-17                 Midlands      3
## 752   2020-07-18                 Midlands      3
## 753   2020-07-19                 Midlands      3
## 754   2020-07-20                 Midlands      3
## 755   2020-07-21                 Midlands      1
## 756   2020-07-22                 Midlands      2
## 757   2020-07-23                 Midlands      6
## 758   2020-07-24                 Midlands      1
## 759   2020-07-25                 Midlands      4
## 760   2020-07-26                 Midlands      4
## 761   2020-07-27                 Midlands      5
## 762   2020-07-28                 Midlands      1
## 763   2020-07-29                 Midlands      1
## 764   2020-07-30                 Midlands      1
## 765   2020-07-31                 Midlands      2
## 766   2020-08-01                 Midlands      0
## 767   2020-08-02                 Midlands      1
## 768   2020-08-03                 Midlands      2
## 769   2020-08-04                 Midlands      1
## 770   2020-08-05                 Midlands      1
## 771   2020-08-06                 Midlands      0
## 772   2020-08-07                 Midlands      3
## 773   2020-08-08                 Midlands      2
## 774   2020-08-09                 Midlands      0
## 775   2020-08-10                 Midlands      0
## 776   2020-08-11                 Midlands      2
## 777   2020-08-12                 Midlands      0
## 778   2020-08-13                 Midlands      0
## 779   2020-08-14                 Midlands      0
## 780   2020-08-15                 Midlands      1
## 781   2020-08-16                 Midlands      0
## 782   2020-08-17                 Midlands      0
## 783   2020-08-18                 Midlands      0
## 784   2020-08-19                 Midlands      0
## 785   2020-08-20                 Midlands      0
## 786   2020-08-21                 Midlands      1
## 787   2020-08-22                 Midlands      0
## 788   2020-08-23                 Midlands      0
## 789   2020-08-24                 Midlands      0
## 790   2020-08-25                 Midlands      2
## 791   2020-08-26                 Midlands      3
## 792   2020-08-27                 Midlands      2
## 793   2020-08-28                 Midlands      1
## 794   2020-08-29                 Midlands      0
## 795   2020-08-30                 Midlands      2
## 796   2020-08-31                 Midlands      1
## 797   2020-09-01                 Midlands      0
## 798   2020-09-02                 Midlands      2
## 799   2020-09-03                 Midlands      0
## 800   2020-09-04                 Midlands      0
## 801   2020-09-05                 Midlands      0
## 802   2020-09-06                 Midlands      1
## 803   2020-09-07                 Midlands      1
## 804   2020-09-08                 Midlands      3
## 805   2020-09-09                 Midlands      0
## 806   2020-09-10                 Midlands      1
## 807   2020-09-11                 Midlands      1
## 808   2020-09-12                 Midlands      2
## 809   2020-09-13                 Midlands      4
## 810   2020-09-14                 Midlands      1
## 811   2020-09-15                 Midlands      2
## 812   2020-09-16                 Midlands      3
## 813   2020-09-17                 Midlands      2
## 814   2020-09-18                 Midlands      5
## 815   2020-09-19                 Midlands      2
## 816   2020-09-20                 Midlands      7
## 817   2020-09-21                 Midlands      3
## 818   2020-09-22                 Midlands      4
## 819   2020-09-23                 Midlands     10
## 820   2020-09-24                 Midlands      7
## 821   2020-09-25                 Midlands      4
## 822   2020-09-26                 Midlands      5
## 823   2020-09-27                 Midlands      9
## 824   2020-09-28                 Midlands      6
## 825   2020-09-29                 Midlands      4
## 826   2020-09-30                 Midlands      5
## 827   2020-10-01                 Midlands      8
## 828   2020-10-02                 Midlands      7
## 829   2020-10-03                 Midlands      6
## 830   2020-10-04                 Midlands      7
## 831   2020-10-05                 Midlands      6
## 832   2020-10-06                 Midlands      5
## 833   2020-10-07                 Midlands      9
## 834   2020-10-08                 Midlands      8
## 835   2020-10-09                 Midlands      7
## 836   2020-10-10                 Midlands      2
## 837   2020-10-11                 Midlands     15
## 838   2020-10-12                 Midlands      7
## 839   2020-10-13                 Midlands     16
## 840   2020-10-14                 Midlands     12
## 841   2020-10-15                 Midlands     11
## 842   2020-10-16                 Midlands     18
## 843   2020-10-17                 Midlands     25
## 844   2020-10-18                 Midlands     11
## 845   2020-10-19                 Midlands     14
## 846   2020-10-20                 Midlands     19
## 847   2020-10-21                 Midlands     15
## 848   2020-10-22                 Midlands     34
## 849   2020-10-23                 Midlands     32
## 850   2020-10-24                 Midlands     24
## 851   2020-10-25                 Midlands     30
## 852   2020-10-26                 Midlands     33
## 853   2020-10-27                 Midlands     38
## 854   2020-10-28                 Midlands     30
## 855   2020-10-29                 Midlands     42
## 856   2020-10-30                 Midlands     42
## 857   2020-10-31                 Midlands     50
## 858   2020-11-01                 Midlands     44
## 859   2020-11-02                 Midlands     58
## 860   2020-11-03                 Midlands     37
## 861   2020-11-04                 Midlands     67
## 862   2020-11-05                 Midlands     50
## 863   2020-11-06                 Midlands     43
## 864   2020-11-07                 Midlands     60
## 865   2020-11-08                 Midlands     55
## 866   2020-11-09                 Midlands     67
## 867   2020-11-10                 Midlands     68
## 868   2020-11-11                 Midlands     56
## 869   2020-11-12                 Midlands     64
## 870   2020-11-13                 Midlands     47
## 871   2020-11-14                 Midlands     66
## 872   2020-11-15                 Midlands     72
## 873   2020-11-16                 Midlands     66
## 874   2020-11-17                 Midlands     66
## 875   2020-11-18                 Midlands     83
## 876   2020-11-19                 Midlands     72
## 877   2020-11-20                 Midlands     87
## 878   2020-11-21                 Midlands     59
## 879   2020-11-22                 Midlands     84
## 880   2020-11-23                 Midlands     80
## 881   2020-11-24                 Midlands     73
## 882   2020-11-25                 Midlands     74
## 883   2020-11-26                 Midlands     77
## 884   2020-11-27                 Midlands     78
## 885   2020-11-28                 Midlands     80
## 886   2020-11-29                 Midlands     85
## 887   2020-11-30                 Midlands     78
## 888   2020-12-01                 Midlands     74
## 889   2020-12-02                 Midlands     64
## 890   2020-12-03                 Midlands     82
## 891   2020-12-04                 Midlands     66
## 892   2020-12-05                 Midlands     71
## 893   2020-12-06                 Midlands     74
## 894   2020-12-07                 Midlands     67
## 895   2020-12-08                 Midlands     64
## 896   2020-12-09                 Midlands     60
## 897   2020-12-10                 Midlands     72
## 898   2020-12-11                 Midlands     65
## 899   2020-12-12                 Midlands     79
## 900   2020-12-13                 Midlands     75
## 901   2020-12-14                 Midlands     76
## 902   2020-12-15                 Midlands     69
## 903   2020-12-16                 Midlands     71
## 904   2020-12-17                 Midlands     83
## 905   2020-12-18                 Midlands     78
## 906   2020-12-19                 Midlands     55
## 907   2020-12-20                 Midlands     66
## 908   2020-12-21                 Midlands     84
## 909   2020-12-22                 Midlands     69
## 910   2020-12-23                 Midlands     56
## 911   2020-12-24                 Midlands     64
## 912   2020-12-25                 Midlands     73
## 913   2020-12-26                 Midlands     61
## 914   2020-12-27                 Midlands     76
## 915   2020-12-28                 Midlands     57
## 916   2020-12-29                 Midlands     66
## 917   2020-12-30                 Midlands     45
## 918   2020-12-31                 Midlands      9
## 919   2020-03-01 North East and Yorkshire      0
## 920   2020-03-02 North East and Yorkshire      0
## 921   2020-03-03 North East and Yorkshire      0
## 922   2020-03-04 North East and Yorkshire      0
## 923   2020-03-05 North East and Yorkshire      0
## 924   2020-03-06 North East and Yorkshire      0
## 925   2020-03-07 North East and Yorkshire      0
## 926   2020-03-08 North East and Yorkshire      0
## 927   2020-03-09 North East and Yorkshire      0
## 928   2020-03-10 North East and Yorkshire      0
## 929   2020-03-11 North East and Yorkshire      0
## 930   2020-03-12 North East and Yorkshire      0
## 931   2020-03-13 North East and Yorkshire      0
## 932   2020-03-14 North East and Yorkshire      0
## 933   2020-03-15 North East and Yorkshire      2
## 934   2020-03-16 North East and Yorkshire      3
## 935   2020-03-17 North East and Yorkshire      1
## 936   2020-03-18 North East and Yorkshire      2
## 937   2020-03-19 North East and Yorkshire      6
## 938   2020-03-20 North East and Yorkshire      5
## 939   2020-03-21 North East and Yorkshire      6
## 940   2020-03-22 North East and Yorkshire      7
## 941   2020-03-23 North East and Yorkshire      9
## 942   2020-03-24 North East and Yorkshire      8
## 943   2020-03-25 North East and Yorkshire     18
## 944   2020-03-26 North East and Yorkshire     21
## 945   2020-03-27 North East and Yorkshire     28
## 946   2020-03-28 North East and Yorkshire     35
## 947   2020-03-29 North East and Yorkshire     38
## 948   2020-03-30 North East and Yorkshire     64
## 949   2020-03-31 North East and Yorkshire     60
## 950   2020-04-01 North East and Yorkshire     67
## 951   2020-04-02 North East and Yorkshire     75
## 952   2020-04-03 North East and Yorkshire    100
## 953   2020-04-04 North East and Yorkshire    105
## 954   2020-04-05 North East and Yorkshire     92
## 955   2020-04-06 North East and Yorkshire     96
## 956   2020-04-07 North East and Yorkshire    102
## 957   2020-04-08 North East and Yorkshire    107
## 958   2020-04-09 North East and Yorkshire    111
## 959   2020-04-10 North East and Yorkshire    117
## 960   2020-04-11 North East and Yorkshire     98
## 961   2020-04-12 North East and Yorkshire     84
## 962   2020-04-13 North East and Yorkshire     94
## 963   2020-04-14 North East and Yorkshire    107
## 964   2020-04-15 North East and Yorkshire     96
## 965   2020-04-16 North East and Yorkshire    103
## 966   2020-04-17 North East and Yorkshire     88
## 967   2020-04-18 North East and Yorkshire     95
## 968   2020-04-19 North East and Yorkshire     88
## 969   2020-04-20 North East and Yorkshire    100
## 970   2020-04-21 North East and Yorkshire     76
## 971   2020-04-22 North East and Yorkshire     84
## 972   2020-04-23 North East and Yorkshire     63
## 973   2020-04-24 North East and Yorkshire     72
## 974   2020-04-25 North East and Yorkshire     69
## 975   2020-04-26 North East and Yorkshire     65
## 976   2020-04-27 North East and Yorkshire     65
## 977   2020-04-28 North East and Yorkshire     57
## 978   2020-04-29 North East and Yorkshire     69
## 979   2020-04-30 North East and Yorkshire     57
## 980   2020-05-01 North East and Yorkshire     64
## 981   2020-05-02 North East and Yorkshire     48
## 982   2020-05-03 North East and Yorkshire     40
## 983   2020-05-04 North East and Yorkshire     49
## 984   2020-05-05 North East and Yorkshire     40
## 985   2020-05-06 North East and Yorkshire     51
## 986   2020-05-07 North East and Yorkshire     45
## 987   2020-05-08 North East and Yorkshire     42
## 988   2020-05-09 North East and Yorkshire     44
## 989   2020-05-10 North East and Yorkshire     40
## 990   2020-05-11 North East and Yorkshire     29
## 991   2020-05-12 North East and Yorkshire     27
## 992   2020-05-13 North East and Yorkshire     28
## 993   2020-05-14 North East and Yorkshire     31
## 994   2020-05-15 North East and Yorkshire     32
## 995   2020-05-16 North East and Yorkshire     35
## 996   2020-05-17 North East and Yorkshire     26
## 997   2020-05-18 North East and Yorkshire     30
## 998   2020-05-19 North East and Yorkshire     27
## 999   2020-05-20 North East and Yorkshire     22
## 1000  2020-05-21 North East and Yorkshire     33
## 1001  2020-05-22 North East and Yorkshire     22
## 1002  2020-05-23 North East and Yorkshire     18
## 1003  2020-05-24 North East and Yorkshire     26
## 1004  2020-05-25 North East and Yorkshire     21
## 1005  2020-05-26 North East and Yorkshire     21
## 1006  2020-05-27 North East and Yorkshire     22
## 1007  2020-05-28 North East and Yorkshire     21
## 1008  2020-05-29 North East and Yorkshire     25
## 1009  2020-05-30 North East and Yorkshire     20
## 1010  2020-05-31 North East and Yorkshire     20
## 1011  2020-06-01 North East and Yorkshire     17
## 1012  2020-06-02 North East and Yorkshire     23
## 1013  2020-06-03 North East and Yorkshire     24
## 1014  2020-06-04 North East and Yorkshire     17
## 1015  2020-06-05 North East and Yorkshire     18
## 1016  2020-06-06 North East and Yorkshire     21
## 1017  2020-06-07 North East and Yorkshire     14
## 1018  2020-06-08 North East and Yorkshire     11
## 1019  2020-06-09 North East and Yorkshire     12
## 1020  2020-06-10 North East and Yorkshire     19
## 1021  2020-06-11 North East and Yorkshire      7
## 1022  2020-06-12 North East and Yorkshire      9
## 1023  2020-06-13 North East and Yorkshire     10
## 1024  2020-06-14 North East and Yorkshire     11
## 1025  2020-06-15 North East and Yorkshire      9
## 1026  2020-06-16 North East and Yorkshire     10
## 1027  2020-06-17 North East and Yorkshire      9
## 1028  2020-06-18 North East and Yorkshire     11
## 1029  2020-06-19 North East and Yorkshire      6
## 1030  2020-06-20 North East and Yorkshire      5
## 1031  2020-06-21 North East and Yorkshire      4
## 1032  2020-06-22 North East and Yorkshire      7
## 1033  2020-06-23 North East and Yorkshire      8
## 1034  2020-06-24 North East and Yorkshire     10
## 1035  2020-06-25 North East and Yorkshire      4
## 1036  2020-06-26 North East and Yorkshire      8
## 1037  2020-06-27 North East and Yorkshire      4
## 1038  2020-06-28 North East and Yorkshire      5
## 1039  2020-06-29 North East and Yorkshire      2
## 1040  2020-06-30 North East and Yorkshire      7
## 1041  2020-07-01 North East and Yorkshire      1
## 1042  2020-07-02 North East and Yorkshire      5
## 1043  2020-07-03 North East and Yorkshire      4
## 1044  2020-07-04 North East and Yorkshire      4
## 1045  2020-07-05 North East and Yorkshire      3
## 1046  2020-07-06 North East and Yorkshire      2
## 1047  2020-07-07 North East and Yorkshire      3
## 1048  2020-07-08 North East and Yorkshire      3
## 1049  2020-07-09 North East and Yorkshire      0
## 1050  2020-07-10 North East and Yorkshire      3
## 1051  2020-07-11 North East and Yorkshire      1
## 1052  2020-07-12 North East and Yorkshire      4
## 1053  2020-07-13 North East and Yorkshire      1
## 1054  2020-07-14 North East and Yorkshire      1
## 1055  2020-07-15 North East and Yorkshire      2
## 1056  2020-07-16 North East and Yorkshire      3
## 1057  2020-07-17 North East and Yorkshire      1
## 1058  2020-07-18 North East and Yorkshire      2
## 1059  2020-07-19 North East and Yorkshire      2
## 1060  2020-07-20 North East and Yorkshire      1
## 1061  2020-07-21 North East and Yorkshire      1
## 1062  2020-07-22 North East and Yorkshire      6
## 1063  2020-07-23 North East and Yorkshire      0
## 1064  2020-07-24 North East and Yorkshire      1
## 1065  2020-07-25 North East and Yorkshire      5
## 1066  2020-07-26 North East and Yorkshire      1
## 1067  2020-07-27 North East and Yorkshire      0
## 1068  2020-07-28 North East and Yorkshire      2
## 1069  2020-07-29 North East and Yorkshire      1
## 1070  2020-07-30 North East and Yorkshire      0
## 1071  2020-07-31 North East and Yorkshire      1
## 1072  2020-08-01 North East and Yorkshire      3
## 1073  2020-08-02 North East and Yorkshire      2
## 1074  2020-08-03 North East and Yorkshire      1
## 1075  2020-08-04 North East and Yorkshire      3
## 1076  2020-08-05 North East and Yorkshire      1
## 1077  2020-08-06 North East and Yorkshire      4
## 1078  2020-08-07 North East and Yorkshire      0
## 1079  2020-08-08 North East and Yorkshire      2
## 1080  2020-08-09 North East and Yorkshire      3
## 1081  2020-08-10 North East and Yorkshire      3
## 1082  2020-08-11 North East and Yorkshire      2
## 1083  2020-08-12 North East and Yorkshire      2
## 1084  2020-08-13 North East and Yorkshire      0
## 1085  2020-08-14 North East and Yorkshire      1
## 1086  2020-08-15 North East and Yorkshire      1
## 1087  2020-08-16 North East and Yorkshire      0
## 1088  2020-08-17 North East and Yorkshire      6
## 1089  2020-08-18 North East and Yorkshire      1
## 1090  2020-08-19 North East and Yorkshire      0
## 1091  2020-08-20 North East and Yorkshire      0
## 1092  2020-08-21 North East and Yorkshire      1
## 1093  2020-08-22 North East and Yorkshire      1
## 1094  2020-08-23 North East and Yorkshire      3
## 1095  2020-08-24 North East and Yorkshire      0
## 1096  2020-08-25 North East and Yorkshire      2
## 1097  2020-08-26 North East and Yorkshire      2
## 1098  2020-08-27 North East and Yorkshire      1
## 1099  2020-08-28 North East and Yorkshire      0
## 1100  2020-08-29 North East and Yorkshire      1
## 1101  2020-08-30 North East and Yorkshire      0
## 1102  2020-08-31 North East and Yorkshire      0
## 1103  2020-09-01 North East and Yorkshire      2
## 1104  2020-09-02 North East and Yorkshire      3
## 1105  2020-09-03 North East and Yorkshire      1
## 1106  2020-09-04 North East and Yorkshire      1
## 1107  2020-09-05 North East and Yorkshire      2
## 1108  2020-09-06 North East and Yorkshire      1
## 1109  2020-09-07 North East and Yorkshire      0
## 1110  2020-09-08 North East and Yorkshire      1
## 1111  2020-09-09 North East and Yorkshire      2
## 1112  2020-09-10 North East and Yorkshire      0
## 1113  2020-09-11 North East and Yorkshire      3
## 1114  2020-09-12 North East and Yorkshire      1
## 1115  2020-09-13 North East and Yorkshire      3
## 1116  2020-09-14 North East and Yorkshire      4
## 1117  2020-09-15 North East and Yorkshire      3
## 1118  2020-09-16 North East and Yorkshire      3
## 1119  2020-09-17 North East and Yorkshire      5
## 1120  2020-09-18 North East and Yorkshire      6
## 1121  2020-09-19 North East and Yorkshire      2
## 1122  2020-09-20 North East and Yorkshire      9
## 1123  2020-09-21 North East and Yorkshire      7
## 1124  2020-09-22 North East and Yorkshire      5
## 1125  2020-09-23 North East and Yorkshire      6
## 1126  2020-09-24 North East and Yorkshire      3
## 1127  2020-09-25 North East and Yorkshire      5
## 1128  2020-09-26 North East and Yorkshire      7
## 1129  2020-09-27 North East and Yorkshire     10
## 1130  2020-09-28 North East and Yorkshire      6
## 1131  2020-09-29 North East and Yorkshire      7
## 1132  2020-09-30 North East and Yorkshire      7
## 1133  2020-10-01 North East and Yorkshire      8
## 1134  2020-10-02 North East and Yorkshire     16
## 1135  2020-10-03 North East and Yorkshire     12
## 1136  2020-10-04 North East and Yorkshire     13
## 1137  2020-10-05 North East and Yorkshire     10
## 1138  2020-10-06 North East and Yorkshire     15
## 1139  2020-10-07 North East and Yorkshire     13
## 1140  2020-10-08 North East and Yorkshire     16
## 1141  2020-10-09 North East and Yorkshire     10
## 1142  2020-10-10 North East and Yorkshire     16
## 1143  2020-10-11 North East and Yorkshire     16
## 1144  2020-10-12 North East and Yorkshire     15
## 1145  2020-10-13 North East and Yorkshire     21
## 1146  2020-10-14 North East and Yorkshire     20
## 1147  2020-10-15 North East and Yorkshire     23
## 1148  2020-10-16 North East and Yorkshire     24
## 1149  2020-10-17 North East and Yorkshire     34
## 1150  2020-10-18 North East and Yorkshire     22
## 1151  2020-10-19 North East and Yorkshire     34
## 1152  2020-10-20 North East and Yorkshire     36
## 1153  2020-10-21 North East and Yorkshire     42
## 1154  2020-10-22 North East and Yorkshire     33
## 1155  2020-10-23 North East and Yorkshire     31
## 1156  2020-10-24 North East and Yorkshire     34
## 1157  2020-10-25 North East and Yorkshire     35
## 1158  2020-10-26 North East and Yorkshire     44
## 1159  2020-10-27 North East and Yorkshire     45
## 1160  2020-10-28 North East and Yorkshire     38
## 1161  2020-10-29 North East and Yorkshire     51
## 1162  2020-10-30 North East and Yorkshire     48
## 1163  2020-10-31 North East and Yorkshire     58
## 1164  2020-11-01 North East and Yorkshire     48
## 1165  2020-11-02 North East and Yorkshire     50
## 1166  2020-11-03 North East and Yorkshire     48
## 1167  2020-11-04 North East and Yorkshire     57
## 1168  2020-11-05 North East and Yorkshire     57
## 1169  2020-11-06 North East and Yorkshire     57
## 1170  2020-11-07 North East and Yorkshire     75
## 1171  2020-11-08 North East and Yorkshire     61
## 1172  2020-11-09 North East and Yorkshire     87
## 1173  2020-11-10 North East and Yorkshire     65
## 1174  2020-11-11 North East and Yorkshire     59
## 1175  2020-11-12 North East and Yorkshire     77
## 1176  2020-11-13 North East and Yorkshire     78
## 1177  2020-11-14 North East and Yorkshire     72
## 1178  2020-11-15 North East and Yorkshire     76
## 1179  2020-11-16 North East and Yorkshire     51
## 1180  2020-11-17 North East and Yorkshire     68
## 1181  2020-11-18 North East and Yorkshire     79
## 1182  2020-11-19 North East and Yorkshire     72
## 1183  2020-11-20 North East and Yorkshire     75
## 1184  2020-11-21 North East and Yorkshire     54
## 1185  2020-11-22 North East and Yorkshire     80
## 1186  2020-11-23 North East and Yorkshire     82
## 1187  2020-11-24 North East and Yorkshire     81
## 1188  2020-11-25 North East and Yorkshire     68
## 1189  2020-11-26 North East and Yorkshire     63
## 1190  2020-11-27 North East and Yorkshire     61
## 1191  2020-11-28 North East and Yorkshire     73
## 1192  2020-11-29 North East and Yorkshire     61
## 1193  2020-11-30 North East and Yorkshire     54
## 1194  2020-12-01 North East and Yorkshire     42
## 1195  2020-12-02 North East and Yorkshire     57
## 1196  2020-12-03 North East and Yorkshire     70
## 1197  2020-12-04 North East and Yorkshire     63
## 1198  2020-12-05 North East and Yorkshire     48
## 1199  2020-12-06 North East and Yorkshire     63
## 1200  2020-12-07 North East and Yorkshire     49
## 1201  2020-12-08 North East and Yorkshire     54
## 1202  2020-12-09 North East and Yorkshire     49
## 1203  2020-12-10 North East and Yorkshire     54
## 1204  2020-12-11 North East and Yorkshire     54
## 1205  2020-12-12 North East and Yorkshire     54
## 1206  2020-12-13 North East and Yorkshire     51
## 1207  2020-12-14 North East and Yorkshire     49
## 1208  2020-12-15 North East and Yorkshire     50
## 1209  2020-12-16 North East and Yorkshire     39
## 1210  2020-12-17 North East and Yorkshire     47
## 1211  2020-12-18 North East and Yorkshire     55
## 1212  2020-12-19 North East and Yorkshire     47
## 1213  2020-12-20 North East and Yorkshire     49
## 1214  2020-12-21 North East and Yorkshire     33
## 1215  2020-12-22 North East and Yorkshire     53
## 1216  2020-12-23 North East and Yorkshire     47
## 1217  2020-12-24 North East and Yorkshire     47
## 1218  2020-12-25 North East and Yorkshire     52
## 1219  2020-12-26 North East and Yorkshire     63
## 1220  2020-12-27 North East and Yorkshire     59
## 1221  2020-12-28 North East and Yorkshire     54
## 1222  2020-12-29 North East and Yorkshire     49
## 1223  2020-12-30 North East and Yorkshire     30
## 1224  2020-12-31 North East and Yorkshire      9
## 1225  2020-03-01               North West      0
## 1226  2020-03-02               North West      0
## 1227  2020-03-03               North West      0
## 1228  2020-03-04               North West      0
## 1229  2020-03-05               North West      1
## 1230  2020-03-06               North West      0
## 1231  2020-03-07               North West      0
## 1232  2020-03-08               North West      1
## 1233  2020-03-09               North West      0
## 1234  2020-03-10               North West      0
## 1235  2020-03-11               North West      0
## 1236  2020-03-12               North West      2
## 1237  2020-03-13               North West      3
## 1238  2020-03-14               North West      1
## 1239  2020-03-15               North West      4
## 1240  2020-03-16               North West      2
## 1241  2020-03-17               North West      4
## 1242  2020-03-18               North West      6
## 1243  2020-03-19               North West      7
## 1244  2020-03-20               North West     10
## 1245  2020-03-21               North West     11
## 1246  2020-03-22               North West     13
## 1247  2020-03-23               North West     15
## 1248  2020-03-24               North West     21
## 1249  2020-03-25               North West     21
## 1250  2020-03-26               North West     29
## 1251  2020-03-27               North West     36
## 1252  2020-03-28               North West     28
## 1253  2020-03-29               North West     46
## 1254  2020-03-30               North West     67
## 1255  2020-03-31               North West     52
## 1256  2020-04-01               North West     86
## 1257  2020-04-02               North West     96
## 1258  2020-04-03               North West     95
## 1259  2020-04-04               North West     98
## 1260  2020-04-05               North West    102
## 1261  2020-04-06               North West    100
## 1262  2020-04-07               North West    136
## 1263  2020-04-08               North West    127
## 1264  2020-04-09               North West    119
## 1265  2020-04-10               North West    117
## 1266  2020-04-11               North West    138
## 1267  2020-04-12               North West    125
## 1268  2020-04-13               North West    130
## 1269  2020-04-14               North West    130
## 1270  2020-04-15               North West    114
## 1271  2020-04-16               North West    135
## 1272  2020-04-17               North West     98
## 1273  2020-04-18               North West    113
## 1274  2020-04-19               North West     71
## 1275  2020-04-20               North West     83
## 1276  2020-04-21               North West     76
## 1277  2020-04-22               North West     86
## 1278  2020-04-23               North West     85
## 1279  2020-04-24               North West     66
## 1280  2020-04-25               North West     66
## 1281  2020-04-26               North West     55
## 1282  2020-04-27               North West     54
## 1283  2020-04-28               North West     57
## 1284  2020-04-29               North West     63
## 1285  2020-04-30               North West     60
## 1286  2020-05-01               North West     45
## 1287  2020-05-02               North West     56
## 1288  2020-05-03               North West     55
## 1289  2020-05-04               North West     48
## 1290  2020-05-05               North West     48
## 1291  2020-05-06               North West     44
## 1292  2020-05-07               North West     49
## 1293  2020-05-08               North West     42
## 1294  2020-05-09               North West     31
## 1295  2020-05-10               North West     42
## 1296  2020-05-11               North West     35
## 1297  2020-05-12               North West     38
## 1298  2020-05-13               North West     25
## 1299  2020-05-14               North West     26
## 1300  2020-05-15               North West     33
## 1301  2020-05-16               North West     32
## 1302  2020-05-17               North West     24
## 1303  2020-05-18               North West     31
## 1304  2020-05-19               North West     35
## 1305  2020-05-20               North West     27
## 1306  2020-05-21               North West     28
## 1307  2020-05-22               North West     26
## 1308  2020-05-23               North West     31
## 1309  2020-05-24               North West     26
## 1310  2020-05-25               North West     31
## 1311  2020-05-26               North West     27
## 1312  2020-05-27               North West     27
## 1313  2020-05-28               North West     28
## 1314  2020-05-29               North West     20
## 1315  2020-05-30               North West     19
## 1316  2020-05-31               North West     13
## 1317  2020-06-01               North West     12
## 1318  2020-06-02               North West     27
## 1319  2020-06-03               North West     22
## 1320  2020-06-04               North West     22
## 1321  2020-06-05               North West     16
## 1322  2020-06-06               North West     26
## 1323  2020-06-07               North West     20
## 1324  2020-06-08               North West     23
## 1325  2020-06-09               North West     17
## 1326  2020-06-10               North West     16
## 1327  2020-06-11               North West     16
## 1328  2020-06-12               North West     11
## 1329  2020-06-13               North West     10
## 1330  2020-06-14               North West     15
## 1331  2020-06-15               North West     16
## 1332  2020-06-16               North West     16
## 1333  2020-06-17               North West     13
## 1334  2020-06-18               North West     14
## 1335  2020-06-19               North West      7
## 1336  2020-06-20               North West     11
## 1337  2020-06-21               North West      8
## 1338  2020-06-22               North West     11
## 1339  2020-06-23               North West     13
## 1340  2020-06-24               North West     13
## 1341  2020-06-25               North West     15
## 1342  2020-06-26               North West      6
## 1343  2020-06-27               North West      7
## 1344  2020-06-28               North West      9
## 1345  2020-06-29               North West      9
## 1346  2020-06-30               North West      7
## 1347  2020-07-01               North West      3
## 1348  2020-07-02               North West      6
## 1349  2020-07-03               North West      7
## 1350  2020-07-04               North West      4
## 1351  2020-07-05               North West      6
## 1352  2020-07-06               North West      9
## 1353  2020-07-07               North West      8
## 1354  2020-07-08               North West      5
## 1355  2020-07-09               North West     10
## 1356  2020-07-10               North West      2
## 1357  2020-07-11               North West      5
## 1358  2020-07-12               North West      0
## 1359  2020-07-13               North West      6
## 1360  2020-07-14               North West      4
## 1361  2020-07-15               North West      5
## 1362  2020-07-16               North West      2
## 1363  2020-07-17               North West      4
## 1364  2020-07-18               North West      5
## 1365  2020-07-19               North West      3
## 1366  2020-07-20               North West      0
## 1367  2020-07-21               North West      2
## 1368  2020-07-22               North West      3
## 1369  2020-07-23               North West      3
## 1370  2020-07-24               North West      1
## 1371  2020-07-25               North West      1
## 1372  2020-07-26               North West      3
## 1373  2020-07-27               North West      1
## 1374  2020-07-28               North West      1
## 1375  2020-07-29               North West      2
## 1376  2020-07-30               North West      2
## 1377  2020-07-31               North West      0
## 1378  2020-08-01               North West      2
## 1379  2020-08-02               North West      1
## 1380  2020-08-03               North West      8
## 1381  2020-08-04               North West      3
## 1382  2020-08-05               North West      2
## 1383  2020-08-06               North West      2
## 1384  2020-08-07               North West      2
## 1385  2020-08-08               North West      2
## 1386  2020-08-09               North West      3
## 1387  2020-08-10               North West      2
## 1388  2020-08-11               North West      3
## 1389  2020-08-12               North West      0
## 1390  2020-08-13               North West      2
## 1391  2020-08-14               North West      2
## 1392  2020-08-15               North West      6
## 1393  2020-08-16               North West      2
## 1394  2020-08-17               North West      1
## 1395  2020-08-18               North West      2
## 1396  2020-08-19               North West      1
## 1397  2020-08-20               North West      1
## 1398  2020-08-21               North West      4
## 1399  2020-08-22               North West      3
## 1400  2020-08-23               North West      5
## 1401  2020-08-24               North West      4
## 1402  2020-08-25               North West      3
## 1403  2020-08-26               North West      4
## 1404  2020-08-27               North West      1
## 1405  2020-08-28               North West      2
## 1406  2020-08-29               North West      0
## 1407  2020-08-30               North West      2
## 1408  2020-08-31               North West      3
## 1409  2020-09-01               North West      0
## 1410  2020-09-02               North West      2
## 1411  2020-09-03               North West      1
## 1412  2020-09-04               North West      3
## 1413  2020-09-05               North West      6
## 1414  2020-09-06               North West      1
## 1415  2020-09-07               North West      8
## 1416  2020-09-08               North West      6
## 1417  2020-09-09               North West      5
## 1418  2020-09-10               North West      5
## 1419  2020-09-11               North West      1
## 1420  2020-09-12               North West      4
## 1421  2020-09-13               North West      2
## 1422  2020-09-14               North West      4
## 1423  2020-09-15               North West      4
## 1424  2020-09-16               North West      6
## 1425  2020-09-17               North West      7
## 1426  2020-09-18               North West      6
## 1427  2020-09-19               North West      3
## 1428  2020-09-20               North West      2
## 1429  2020-09-21               North West      2
## 1430  2020-09-22               North West      9
## 1431  2020-09-23               North West     14
## 1432  2020-09-24               North West     10
## 1433  2020-09-25               North West      8
## 1434  2020-09-26               North West     14
## 1435  2020-09-27               North West     11
## 1436  2020-09-28               North West     15
## 1437  2020-09-29               North West     12
## 1438  2020-09-30               North West     17
## 1439  2020-10-01               North West     17
## 1440  2020-10-02               North West     20
## 1441  2020-10-03               North West     15
## 1442  2020-10-04               North West     15
## 1443  2020-10-05               North West     15
## 1444  2020-10-06               North West     20
## 1445  2020-10-07               North West     20
## 1446  2020-10-08               North West     22
## 1447  2020-10-09               North West     23
## 1448  2020-10-10               North West     31
## 1449  2020-10-11               North West     31
## 1450  2020-10-12               North West     35
## 1451  2020-10-13               North West     26
## 1452  2020-10-14               North West     35
## 1453  2020-10-15               North West     36
## 1454  2020-10-16               North West     34
## 1455  2020-10-17               North West     52
## 1456  2020-10-18               North West     40
## 1457  2020-10-19               North West     43
## 1458  2020-10-20               North West     48
## 1459  2020-10-21               North West     51
## 1460  2020-10-22               North West     49
## 1461  2020-10-23               North West     50
## 1462  2020-10-24               North West     51
## 1463  2020-10-25               North West     63
## 1464  2020-10-26               North West     53
## 1465  2020-10-27               North West     49
## 1466  2020-10-28               North West     57
## 1467  2020-10-29               North West     74
## 1468  2020-10-30               North West     73
## 1469  2020-10-31               North West     63
## 1470  2020-11-01               North West     76
## 1471  2020-11-02               North West     65
## 1472  2020-11-03               North West     76
## 1473  2020-11-04               North West     64
## 1474  2020-11-05               North West     67
## 1475  2020-11-06               North West     75
## 1476  2020-11-07               North West     79
## 1477  2020-11-08               North West     83
## 1478  2020-11-09               North West     82
## 1479  2020-11-10               North West     68
## 1480  2020-11-11               North West     61
## 1481  2020-11-12               North West     64
## 1482  2020-11-13               North West     81
## 1483  2020-11-14               North West     61
## 1484  2020-11-15               North West     75
## 1485  2020-11-16               North West     74
## 1486  2020-11-17               North West     73
## 1487  2020-11-18               North West     70
## 1488  2020-11-19               North West     67
## 1489  2020-11-20               North West     52
## 1490  2020-11-21               North West     68
## 1491  2020-11-22               North West     52
## 1492  2020-11-23               North West     54
## 1493  2020-11-24               North West     64
## 1494  2020-11-25               North West     65
## 1495  2020-11-26               North West     53
## 1496  2020-11-27               North West     50
## 1497  2020-11-28               North West     46
## 1498  2020-11-29               North West     53
## 1499  2020-11-30               North West     48
## 1500  2020-12-01               North West     53
## 1501  2020-12-02               North West     48
## 1502  2020-12-03               North West     46
## 1503  2020-12-04               North West     46
## 1504  2020-12-05               North West     37
## 1505  2020-12-06               North West     42
## 1506  2020-12-07               North West     50
## 1507  2020-12-08               North West     48
## 1508  2020-12-09               North West     47
## 1509  2020-12-10               North West     47
## 1510  2020-12-11               North West     41
## 1511  2020-12-12               North West     47
## 1512  2020-12-13               North West     38
## 1513  2020-12-14               North West     49
## 1514  2020-12-15               North West     33
## 1515  2020-12-16               North West     39
## 1516  2020-12-17               North West     25
## 1517  2020-12-18               North West     47
## 1518  2020-12-19               North West     45
## 1519  2020-12-20               North West     36
## 1520  2020-12-21               North West     49
## 1521  2020-12-22               North West     51
## 1522  2020-12-23               North West     46
## 1523  2020-12-24               North West     54
## 1524  2020-12-25               North West     51
## 1525  2020-12-26               North West     54
## 1526  2020-12-27               North West     46
## 1527  2020-12-28               North West     42
## 1528  2020-12-29               North West     37
## 1529  2020-12-30               North West     35
## 1530  2020-12-31               North West     10
## 1531  2020-03-01               South East      0
## 1532  2020-03-02               South East      0
## 1533  2020-03-03               South East      1
## 1534  2020-03-04               South East      0
## 1535  2020-03-05               South East      1
## 1536  2020-03-06               South East      0
## 1537  2020-03-07               South East      0
## 1538  2020-03-08               South East      1
## 1539  2020-03-09               South East      1
## 1540  2020-03-10               South East      1
## 1541  2020-03-11               South East      1
## 1542  2020-03-12               South East      0
## 1543  2020-03-13               South East      1
## 1544  2020-03-14               South East      1
## 1545  2020-03-15               South East      5
## 1546  2020-03-16               South East      8
## 1547  2020-03-17               South East      7
## 1548  2020-03-18               South East     10
## 1549  2020-03-19               South East      9
## 1550  2020-03-20               South East     13
## 1551  2020-03-21               South East      7
## 1552  2020-03-22               South East     25
## 1553  2020-03-23               South East     20
## 1554  2020-03-24               South East     22
## 1555  2020-03-25               South East     29
## 1556  2020-03-26               South East     35
## 1557  2020-03-27               South East     36
## 1558  2020-03-28               South East     36
## 1559  2020-03-29               South East     55
## 1560  2020-03-30               South East     58
## 1561  2020-03-31               South East     65
## 1562  2020-04-01               South East     66
## 1563  2020-04-02               South East     55
## 1564  2020-04-03               South East     72
## 1565  2020-04-04               South East     80
## 1566  2020-04-05               South East     82
## 1567  2020-04-06               South East     88
## 1568  2020-04-07               South East    100
## 1569  2020-04-08               South East     83
## 1570  2020-04-09               South East    104
## 1571  2020-04-10               South East     88
## 1572  2020-04-11               South East     88
## 1573  2020-04-12               South East     88
## 1574  2020-04-13               South East     84
## 1575  2020-04-14               South East     65
## 1576  2020-04-15               South East     72
## 1577  2020-04-16               South East     56
## 1578  2020-04-17               South East     86
## 1579  2020-04-18               South East     57
## 1580  2020-04-19               South East     70
## 1581  2020-04-20               South East     87
## 1582  2020-04-21               South East     51
## 1583  2020-04-22               South East     54
## 1584  2020-04-23               South East     57
## 1585  2020-04-24               South East     64
## 1586  2020-04-25               South East     51
## 1587  2020-04-26               South East     51
## 1588  2020-04-27               South East     41
## 1589  2020-04-28               South East     40
## 1590  2020-04-29               South East     47
## 1591  2020-04-30               South East     29
## 1592  2020-05-01               South East     37
## 1593  2020-05-02               South East     36
## 1594  2020-05-03               South East     17
## 1595  2020-05-04               South East     35
## 1596  2020-05-05               South East     29
## 1597  2020-05-06               South East     25
## 1598  2020-05-07               South East     27
## 1599  2020-05-08               South East     26
## 1600  2020-05-09               South East     28
## 1601  2020-05-10               South East     19
## 1602  2020-05-11               South East     25
## 1603  2020-05-12               South East     27
## 1604  2020-05-13               South East     18
## 1605  2020-05-14               South East     32
## 1606  2020-05-15               South East     25
## 1607  2020-05-16               South East     22
## 1608  2020-05-17               South East     18
## 1609  2020-05-18               South East     22
## 1610  2020-05-19               South East     12
## 1611  2020-05-20               South East     22
## 1612  2020-05-21               South East     15
## 1613  2020-05-22               South East     17
## 1614  2020-05-23               South East     21
## 1615  2020-05-24               South East     17
## 1616  2020-05-25               South East     13
## 1617  2020-05-26               South East     19
## 1618  2020-05-27               South East     19
## 1619  2020-05-28               South East     12
## 1620  2020-05-29               South East     22
## 1621  2020-05-30               South East      8
## 1622  2020-05-31               South East     12
## 1623  2020-06-01               South East     11
## 1624  2020-06-02               South East     13
## 1625  2020-06-03               South East     18
## 1626  2020-06-04               South East     11
## 1627  2020-06-05               South East     11
## 1628  2020-06-06               South East     10
## 1629  2020-06-07               South East     12
## 1630  2020-06-08               South East      8
## 1631  2020-06-09               South East     10
## 1632  2020-06-10               South East     11
## 1633  2020-06-11               South East      5
## 1634  2020-06-12               South East      6
## 1635  2020-06-13               South East      7
## 1636  2020-06-14               South East      7
## 1637  2020-06-15               South East      8
## 1638  2020-06-16               South East     14
## 1639  2020-06-17               South East      9
## 1640  2020-06-18               South East      4
## 1641  2020-06-19               South East      7
## 1642  2020-06-20               South East      5
## 1643  2020-06-21               South East      3
## 1644  2020-06-22               South East      2
## 1645  2020-06-23               South East      9
## 1646  2020-06-24               South East      7
## 1647  2020-06-25               South East      5
## 1648  2020-06-26               South East      8
## 1649  2020-06-27               South East      9
## 1650  2020-06-28               South East      6
## 1651  2020-06-29               South East      5
## 1652  2020-06-30               South East      5
## 1653  2020-07-01               South East      2
## 1654  2020-07-02               South East      8
## 1655  2020-07-03               South East      3
## 1656  2020-07-04               South East      6
## 1657  2020-07-05               South East      5
## 1658  2020-07-06               South East      4
## 1659  2020-07-07               South East      6
## 1660  2020-07-08               South East      3
## 1661  2020-07-09               South East      7
## 1662  2020-07-10               South East      3
## 1663  2020-07-11               South East      4
## 1664  2020-07-12               South East      5
## 1665  2020-07-13               South East      5
## 1666  2020-07-14               South East      5
## 1667  2020-07-15               South East      6
## 1668  2020-07-16               South East      3
## 1669  2020-07-17               South East      1
## 1670  2020-07-18               South East      5
## 1671  2020-07-19               South East      2
## 1672  2020-07-20               South East      6
## 1673  2020-07-21               South East      4
## 1674  2020-07-22               South East      2
## 1675  2020-07-23               South East      3
## 1676  2020-07-24               South East      1
## 1677  2020-07-25               South East      1
## 1678  2020-07-26               South East      3
## 1679  2020-07-27               South East      1
## 1680  2020-07-28               South East      3
## 1681  2020-07-29               South East      2
## 1682  2020-07-30               South East      3
## 1683  2020-07-31               South East      1
## 1684  2020-08-01               South East      2
## 1685  2020-08-02               South East      4
## 1686  2020-08-03               South East      0
## 1687  2020-08-04               South East      0
## 1688  2020-08-05               South East      0
## 1689  2020-08-06               South East      2
## 1690  2020-08-07               South East      0
## 1691  2020-08-08               South East      2
## 1692  2020-08-09               South East      0
## 1693  2020-08-10               South East      2
## 1694  2020-08-11               South East      1
## 1695  2020-08-12               South East      1
## 1696  2020-08-13               South East      0
## 1697  2020-08-14               South East      0
## 1698  2020-08-15               South East      2
## 1699  2020-08-16               South East      1
## 1700  2020-08-17               South East      0
## 1701  2020-08-18               South East      2
## 1702  2020-08-19               South East      1
## 1703  2020-08-20               South East      0
## 1704  2020-08-21               South East      0
## 1705  2020-08-22               South East      0
## 1706  2020-08-23               South East      1
## 1707  2020-08-24               South East      0
## 1708  2020-08-25               South East      1
## 1709  2020-08-26               South East      0
## 1710  2020-08-27               South East      1
## 1711  2020-08-28               South East      2
## 1712  2020-08-29               South East      1
## 1713  2020-08-30               South East      0
## 1714  2020-08-31               South East      2
## 1715  2020-09-01               South East      1
## 1716  2020-09-02               South East      1
## 1717  2020-09-03               South East      0
## 1718  2020-09-04               South East      1
## 1719  2020-09-05               South East      0
## 1720  2020-09-06               South East      1
## 1721  2020-09-07               South East      0
## 1722  2020-09-08               South East      0
## 1723  2020-09-09               South East      0
## 1724  2020-09-10               South East      1
## 1725  2020-09-11               South East      1
## 1726  2020-09-12               South East      0
## 1727  2020-09-13               South East      3
## 1728  2020-09-14               South East      1
## 1729  2020-09-15               South East      2
## 1730  2020-09-16               South East      2
## 1731  2020-09-17               South East      3
## 1732  2020-09-18               South East      1
## 1733  2020-09-19               South East      1
## 1734  2020-09-20               South East      0
## 1735  2020-09-21               South East      3
## 1736  2020-09-22               South East      0
## 1737  2020-09-23               South East      2
## 1738  2020-09-24               South East      1
## 1739  2020-09-25               South East      3
## 1740  2020-09-26               South East      2
## 1741  2020-09-27               South East      2
## 1742  2020-09-28               South East      6
## 1743  2020-09-29               South East      3
## 1744  2020-09-30               South East      4
## 1745  2020-10-01               South East      4
## 1746  2020-10-02               South East      2
## 1747  2020-10-03               South East      1
## 1748  2020-10-04               South East      1
## 1749  2020-10-05               South East      2
## 1750  2020-10-06               South East      1
## 1751  2020-10-07               South East      4
## 1752  2020-10-08               South East      1
## 1753  2020-10-09               South East      1
## 1754  2020-10-10               South East      3
## 1755  2020-10-11               South East      3
## 1756  2020-10-12               South East      4
## 1757  2020-10-13               South East      2
## 1758  2020-10-14               South East      2
## 1759  2020-10-15               South East      3
## 1760  2020-10-16               South East      2
## 1761  2020-10-17               South East      3
## 1762  2020-10-18               South East      4
## 1763  2020-10-19               South East      7
## 1764  2020-10-20               South East      8
## 1765  2020-10-21               South East      9
## 1766  2020-10-22               South East      5
## 1767  2020-10-23               South East      7
## 1768  2020-10-24               South East      5
## 1769  2020-10-25               South East      9
## 1770  2020-10-26               South East     13
## 1771  2020-10-27               South East     10
## 1772  2020-10-28               South East     10
## 1773  2020-10-29               South East      7
## 1774  2020-10-30               South East      6
## 1775  2020-10-31               South East     15
## 1776  2020-11-01               South East     18
## 1777  2020-11-02               South East     13
## 1778  2020-11-03               South East     16
## 1779  2020-11-04               South East     10
## 1780  2020-11-05               South East     10
## 1781  2020-11-06               South East     16
## 1782  2020-11-07               South East     17
## 1783  2020-11-08               South East     18
## 1784  2020-11-09               South East     19
## 1785  2020-11-10               South East     20
## 1786  2020-11-11               South East     19
## 1787  2020-11-12               South East     20
## 1788  2020-11-13               South East     12
## 1789  2020-11-14               South East     24
## 1790  2020-11-15               South East     25
## 1791  2020-11-16               South East     22
## 1792  2020-11-17               South East     23
## 1793  2020-11-18               South East     26
## 1794  2020-11-19               South East     21
## 1795  2020-11-20               South East     18
## 1796  2020-11-21               South East     23
## 1797  2020-11-22               South East     30
## 1798  2020-11-23               South East     28
## 1799  2020-11-24               South East     26
## 1800  2020-11-25               South East     42
## 1801  2020-11-26               South East     30
## 1802  2020-11-27               South East     31
## 1803  2020-11-28               South East     24
## 1804  2020-11-29               South East     37
## 1805  2020-11-30               South East     22
## 1806  2020-12-01               South East     29
## 1807  2020-12-02               South East     33
## 1808  2020-12-03               South East     36
## 1809  2020-12-04               South East     40
## 1810  2020-12-05               South East     34
## 1811  2020-12-06               South East     31
## 1812  2020-12-07               South East     24
## 1813  2020-12-08               South East     43
## 1814  2020-12-09               South East     44
## 1815  2020-12-10               South East     36
## 1816  2020-12-11               South East     45
## 1817  2020-12-12               South East     36
## 1818  2020-12-13               South East     31
## 1819  2020-12-14               South East     32
## 1820  2020-12-15               South East     47
## 1821  2020-12-16               South East     41
## 1822  2020-12-17               South East     46
## 1823  2020-12-18               South East     39
## 1824  2020-12-19               South East     36
## 1825  2020-12-20               South East     45
## 1826  2020-12-21               South East     55
## 1827  2020-12-22               South East     51
## 1828  2020-12-23               South East     57
## 1829  2020-12-24               South East     41
## 1830  2020-12-25               South East     51
## 1831  2020-12-26               South East     58
## 1832  2020-12-27               South East     60
## 1833  2020-12-28               South East     70
## 1834  2020-12-29               South East     64
## 1835  2020-12-30               South East     43
## 1836  2020-12-31               South East      3
## 1837  2020-03-01               South West      0
## 1838  2020-03-02               South West      0
## 1839  2020-03-03               South West      0
## 1840  2020-03-04               South West      0
## 1841  2020-03-05               South West      0
## 1842  2020-03-06               South West      0
## 1843  2020-03-07               South West      0
## 1844  2020-03-08               South West      0
## 1845  2020-03-09               South West      0
## 1846  2020-03-10               South West      0
## 1847  2020-03-11               South West      1
## 1848  2020-03-12               South West      0
## 1849  2020-03-13               South West      0
## 1850  2020-03-14               South West      1
## 1851  2020-03-15               South West      0
## 1852  2020-03-16               South West      0
## 1853  2020-03-17               South West      2
## 1854  2020-03-18               South West      2
## 1855  2020-03-19               South West      4
## 1856  2020-03-20               South West      3
## 1857  2020-03-21               South West      6
## 1858  2020-03-22               South West      7
## 1859  2020-03-23               South West      8
## 1860  2020-03-24               South West      7
## 1861  2020-03-25               South West      9
## 1862  2020-03-26               South West     11
## 1863  2020-03-27               South West     13
## 1864  2020-03-28               South West     21
## 1865  2020-03-29               South West     18
## 1866  2020-03-30               South West     23
## 1867  2020-03-31               South West     23
## 1868  2020-04-01               South West     21
## 1869  2020-04-02               South West     23
## 1870  2020-04-03               South West     30
## 1871  2020-04-04               South West     42
## 1872  2020-04-05               South West     32
## 1873  2020-04-06               South West     34
## 1874  2020-04-07               South West     39
## 1875  2020-04-08               South West     47
## 1876  2020-04-09               South West     24
## 1877  2020-04-10               South West     46
## 1878  2020-04-11               South West     43
## 1879  2020-04-12               South West     23
## 1880  2020-04-13               South West     27
## 1881  2020-04-14               South West     24
## 1882  2020-04-15               South West     32
## 1883  2020-04-16               South West     29
## 1884  2020-04-17               South West     33
## 1885  2020-04-18               South West     25
## 1886  2020-04-19               South West     31
## 1887  2020-04-20               South West     26
## 1888  2020-04-21               South West     26
## 1889  2020-04-22               South West     23
## 1890  2020-04-23               South West     17
## 1891  2020-04-24               South West     19
## 1892  2020-04-25               South West     15
## 1893  2020-04-26               South West     27
## 1894  2020-04-27               South West     13
## 1895  2020-04-28               South West     17
## 1896  2020-04-29               South West     15
## 1897  2020-04-30               South West     26
## 1898  2020-05-01               South West      6
## 1899  2020-05-02               South West      7
## 1900  2020-05-03               South West     10
## 1901  2020-05-04               South West     17
## 1902  2020-05-05               South West     14
## 1903  2020-05-06               South West     19
## 1904  2020-05-07               South West     16
## 1905  2020-05-08               South West      6
## 1906  2020-05-09               South West     11
## 1907  2020-05-10               South West      5
## 1908  2020-05-11               South West      8
## 1909  2020-05-12               South West      7
## 1910  2020-05-13               South West      7
## 1911  2020-05-14               South West      6
## 1912  2020-05-15               South West      4
## 1913  2020-05-16               South West      4
## 1914  2020-05-17               South West      6
## 1915  2020-05-18               South West      4
## 1916  2020-05-19               South West      6
## 1917  2020-05-20               South West      1
## 1918  2020-05-21               South West      9
## 1919  2020-05-22               South West      7
## 1920  2020-05-23               South West      6
## 1921  2020-05-24               South West      3
## 1922  2020-05-25               South West      8
## 1923  2020-05-26               South West     11
## 1924  2020-05-27               South West      5
## 1925  2020-05-28               South West     10
## 1926  2020-05-29               South West      7
## 1927  2020-05-30               South West      3
## 1928  2020-05-31               South West      2
## 1929  2020-06-01               South West      7
## 1930  2020-06-02               South West      2
## 1931  2020-06-03               South West      7
## 1932  2020-06-04               South West      2
## 1933  2020-06-05               South West      2
## 1934  2020-06-06               South West      1
## 1935  2020-06-07               South West      3
## 1936  2020-06-08               South West      3
## 1937  2020-06-09               South West      0
## 1938  2020-06-10               South West      1
## 1939  2020-06-11               South West      2
## 1940  2020-06-12               South West      2
## 1941  2020-06-13               South West      2
## 1942  2020-06-14               South West      0
## 1943  2020-06-15               South West      2
## 1944  2020-06-16               South West      2
## 1945  2020-06-17               South West      0
## 1946  2020-06-18               South West      0
## 1947  2020-06-19               South West      0
## 1948  2020-06-20               South West      2
## 1949  2020-06-21               South West      0
## 1950  2020-06-22               South West      1
## 1951  2020-06-23               South West      1
## 1952  2020-06-24               South West      1
## 1953  2020-06-25               South West      0
## 1954  2020-06-26               South West      3
## 1955  2020-06-27               South West      0
## 1956  2020-06-28               South West      0
## 1957  2020-06-29               South West      1
## 1958  2020-06-30               South West      0
## 1959  2020-07-01               South West      0
## 1960  2020-07-02               South West      0
## 1961  2020-07-03               South West      0
## 1962  2020-07-04               South West      0
## 1963  2020-07-05               South West      1
## 1964  2020-07-06               South West      0
## 1965  2020-07-07               South West      0
## 1966  2020-07-08               South West      2
## 1967  2020-07-09               South West      0
## 1968  2020-07-10               South West      1
## 1969  2020-07-11               South West      0
## 1970  2020-07-12               South West      0
## 1971  2020-07-13               South West      1
## 1972  2020-07-14               South West      0
## 1973  2020-07-15               South West      0
## 1974  2020-07-16               South West      0
## 1975  2020-07-17               South West      1
## 1976  2020-07-18               South West      0
## 1977  2020-07-19               South West      0
## 1978  2020-07-20               South West      0
## 1979  2020-07-21               South West      0
## 1980  2020-07-22               South West      0
## 1981  2020-07-23               South West      0
## 1982  2020-07-24               South West      0
## 1983  2020-07-25               South West      0
## 1984  2020-07-26               South West      0
## 1985  2020-07-27               South West      0
## 1986  2020-07-28               South West      0
## 1987  2020-07-29               South West      0
## 1988  2020-07-30               South West      1
## 1989  2020-07-31               South West      0
## 1990  2020-08-01               South West      0
## 1991  2020-08-02               South West      0
## 1992  2020-08-03               South West      0
## 1993  2020-08-04               South West      0
## 1994  2020-08-05               South West      0
## 1995  2020-08-06               South West      0
## 1996  2020-08-07               South West      0
## 1997  2020-08-08               South West      0
## 1998  2020-08-09               South West      0
## 1999  2020-08-10               South West      0
## 2000  2020-08-11               South West      0
## 2001  2020-08-12               South West      0
## 2002  2020-08-13               South West      0
## 2003  2020-08-14               South West      1
## 2004  2020-08-15               South West      0
## 2005  2020-08-16               South West      0
## 2006  2020-08-17               South West      2
## 2007  2020-08-18               South West      0
## 2008  2020-08-19               South West      0
## 2009  2020-08-20               South West      0
## 2010  2020-08-21               South West      0
## 2011  2020-08-22               South West      0
## 2012  2020-08-23               South West      0
## 2013  2020-08-24               South West      0
## 2014  2020-08-25               South West      1
## 2015  2020-08-26               South West      0
## 2016  2020-08-27               South West      1
## 2017  2020-08-28               South West      0
## 2018  2020-08-29               South West      0
## 2019  2020-08-30               South West      0
## 2020  2020-08-31               South West      0
## 2021  2020-09-01               South West      0
## 2022  2020-09-02               South West      0
## 2023  2020-09-03               South West      0
## 2024  2020-09-04               South West      0
## 2025  2020-09-05               South West      0
## 2026  2020-09-06               South West      0
## 2027  2020-09-07               South West      0
## 2028  2020-09-08               South West      1
## 2029  2020-09-09               South West      0
## 2030  2020-09-10               South West      0
## 2031  2020-09-11               South West      0
## 2032  2020-09-12               South West      0
## 2033  2020-09-13               South West      1
## 2034  2020-09-14               South West      0
## 2035  2020-09-15               South West      0
## 2036  2020-09-16               South West      0
## 2037  2020-09-17               South West      1
## 2038  2020-09-18               South West      0
## 2039  2020-09-19               South West      0
## 2040  2020-09-20               South West      1
## 2041  2020-09-21               South West      0
## 2042  2020-09-22               South West      0
## 2043  2020-09-23               South West      0
## 2044  2020-09-24               South West      1
## 2045  2020-09-25               South West      0
## 2046  2020-09-26               South West      0
## 2047  2020-09-27               South West      0
## 2048  2020-09-28               South West      0
## 2049  2020-09-29               South West      0
## 2050  2020-09-30               South West      0
## 2051  2020-10-01               South West      0
## 2052  2020-10-02               South West      1
## 2053  2020-10-03               South West      0
## 2054  2020-10-04               South West      0
## 2055  2020-10-05               South West      0
## 2056  2020-10-06               South West      1
## 2057  2020-10-07               South West      0
## 2058  2020-10-08               South West      1
## 2059  2020-10-09               South West      1
## 2060  2020-10-10               South West      0
## 2061  2020-10-11               South West      4
## 2062  2020-10-12               South West      2
## 2063  2020-10-13               South West      0
## 2064  2020-10-14               South West      3
## 2065  2020-10-15               South West      1
## 2066  2020-10-16               South West      2
## 2067  2020-10-17               South West      8
## 2068  2020-10-18               South West      2
## 2069  2020-10-19               South West      2
## 2070  2020-10-20               South West      3
## 2071  2020-10-21               South West      6
## 2072  2020-10-22               South West      6
## 2073  2020-10-23               South West      5
## 2074  2020-10-24               South West      5
## 2075  2020-10-25               South West      5
## 2076  2020-10-26               South West      7
## 2077  2020-10-27               South West      6
## 2078  2020-10-28               South West      8
## 2079  2020-10-29               South West     11
## 2080  2020-10-30               South West      8
## 2081  2020-10-31               South West      4
## 2082  2020-11-01               South West      5
## 2083  2020-11-02               South West     11
## 2084  2020-11-03               South West      7
## 2085  2020-11-04               South West      8
## 2086  2020-11-05               South West      5
## 2087  2020-11-06               South West     11
## 2088  2020-11-07               South West     10
## 2089  2020-11-08               South West     10
## 2090  2020-11-09               South West     12
## 2091  2020-11-10               South West      6
## 2092  2020-11-11               South West     13
## 2093  2020-11-12               South West     17
## 2094  2020-11-13               South West      9
## 2095  2020-11-14               South West      8
## 2096  2020-11-15               South West     16
## 2097  2020-11-16               South West     18
## 2098  2020-11-17               South West     17
## 2099  2020-11-18               South West     26
## 2100  2020-11-19               South West     15
## 2101  2020-11-20               South West     25
## 2102  2020-11-21               South West     25
## 2103  2020-11-22               South West     23
## 2104  2020-11-23               South West     14
## 2105  2020-11-24               South West     20
## 2106  2020-11-25               South West     25
## 2107  2020-11-26               South West     16
## 2108  2020-11-27               South West     21
## 2109  2020-11-28               South West     35
## 2110  2020-11-29               South West     15
## 2111  2020-11-30               South West     21
## 2112  2020-12-01               South West     18
## 2113  2020-12-02               South West     15
## 2114  2020-12-03               South West     14
## 2115  2020-12-04               South West     19
## 2116  2020-12-05               South West     17
## 2117  2020-12-06               South West     13
## 2118  2020-12-07               South West     14
## 2119  2020-12-08               South West     18
## 2120  2020-12-09               South West     21
## 2121  2020-12-10               South West     20
## 2122  2020-12-11               South West     19
## 2123  2020-12-12               South West     15
## 2124  2020-12-13               South West     19
## 2125  2020-12-14               South West     19
## 2126  2020-12-15               South West     17
## 2127  2020-12-16               South West      8
## 2128  2020-12-17               South West     24
## 2129  2020-12-18               South West      8
## 2130  2020-12-19               South West     20
## 2131  2020-12-20               South West     17
## 2132  2020-12-21               South West     20
## 2133  2020-12-22               South West     10
## 2134  2020-12-23               South West     13
## 2135  2020-12-24               South West     15
## 2136  2020-12-25               South West     17
## 2137  2020-12-26               South West     19
## 2138  2020-12-27               South West     18
## 2139  2020-12-28               South West     16
## 2140  2020-12-29               South West     16
## 2141  2020-12-30               South West      8
## 2142  2020-12-31               South West      3

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2020-12-30"

The completion date of the NHS Pathways data is Wednesday 30 Dec 2020.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 16 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 16 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -16.782  -11.040   -4.389    7.969   19.094  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.530e+00  6.694e-02   67.67   <2e-16 ***
## note_lag    1.685e-05  9.059e-07   18.60   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 98.06949)
## 
##     Null deviance: 49689  on 251  degrees of freedom
## Residual deviance: 25356  on 250  degrees of freedom
##   (16 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 5

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##   92.763144    1.000017
exp(confint(lag_mod))
##                 2.5 %     97.5 %
## (Intercept) 81.153205 105.515059
## note_lag     1.000015   1.000019

Rsq(lag_mod)
## [1] 0.4897147

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                              sysname 
##                                                                                             "Darwin" 
##                                                                                              release 
##                                                                                             "19.6.0" 
##                                                                                              version 
## "Darwin Kernel Version 19.6.0: Thu Oct 29 22:56:45 PDT 2020; root:xnu-6153.141.2.2~1/RELEASE_X86_64" 
##                                                                                             nodename 
##                                                                            "Mac-1609582360628.local" 
##                                                                                              machine 
##                                                                                             "x86_64" 
##                                                                                                login 
##                                                                                               "root" 
##                                                                                                 user 
##                                                                                             "runner" 
##                                                                                       effective_user 
##                                                                                             "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin17.0     
## arch           x86_64                      
## os             darwin17.0                  
## system         x86_64, darwin17.0          
## status                                     
## major          4                           
## minor          0.3                         
## year           2020                        
## month          10                          
## day            10                          
## svn rev        79318                       
## language       R                           
## version.string R version 4.0.3 (2020-10-10)
## nickname       Bunny-Wunnies Freak Out

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 4.0.3 (2020-10-10)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.7
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.4     ggpubr_0.4.0         lubridate_1.7.9.2   
##  [4] chngpt_2020.10-12    cyphr_1.1.0          DT_0.16             
##  [7] kableExtra_1.3.1     janitor_2.0.1        remotes_2.2.0       
## [10] projections_0.5.2    earlyR_0.0.5         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.3      rio_0.5.16          
## [16] reshape2_1.4.4       rvest_0.3.6          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.0        stringr_1.4.0       
## [22] dplyr_1.0.2          purrr_0.3.4          readr_1.4.0         
## [25] tidyr_1.1.2          tibble_3.0.4         ggplot2_3.3.3       
## [28] tidyverse_1.3.0      here_1.0.1           reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] minqa_1.2.4       colorspace_2.0-0  selectr_0.4-2     ggsignif_0.6.0   
##  [5] ellipsis_0.3.1    rprojroot_2.0.2   snakecase_0.11.0  fs_1.5.0         
##  [9] rstudioapi_0.13   farver_2.0.3      fansi_0.4.1       splines_4.0.3    
## [13] knitr_1.30        jsonlite_1.7.2    nloptr_1.2.2.2    broom_0.7.3      
## [17] dbplyr_2.0.0      compiler_4.0.3    httr_1.4.2        backports_1.2.1  
## [21] assertthat_0.2.1  Matrix_1.2-18     cli_2.2.0         htmltools_0.5.0  
## [25] tools_4.0.3       gtable_0.3.0      glue_1.4.2        Rcpp_1.0.5       
## [29] carData_3.0-4     cellranger_1.1.0  vctrs_0.3.6       nlme_3.1-149     
## [33] matchmaker_0.1.1  crosstalk_1.1.0.1 xfun_0.19         ps_1.5.0         
## [37] openxlsx_4.2.3    lme4_1.1-26       lifecycle_0.2.0   statmod_1.4.35   
## [41] rstatix_0.6.0     MASS_7.3-53       scales_1.1.1      hms_0.5.3        
## [45] parallel_4.0.3    sodium_1.1        yaml_2.2.1        curl_4.3         
## [49] gridExtra_2.3     stringi_1.5.3     kyotil_2020.10-12 boot_1.3-25      
## [53] zip_2.1.1         rlang_0.4.10      pkgconfig_2.0.3   evaluate_0.14    
## [57] lattice_0.20-41   labeling_0.4.2    htmlwidgets_1.5.3 cowplot_1.1.1    
## [61] tidyselect_1.1.0  plyr_1.8.6        magrittr_2.0.1    R6_2.5.0         
## [65] generics_0.1.0    DBI_1.1.0         pillar_1.4.7      haven_2.3.1      
## [69] foreign_0.8-80    withr_2.3.0       mgcv_1.8-33       survival_3.2-7   
## [73] abind_1.4-5       modelr_0.1.8      crayon_1.3.4      car_3.0-10       
## [77] utf8_1.1.4        rmarkdown_2.6     viridis_0.5.1     grid_4.0.3       
## [81] readxl_1.3.1      data.table_1.13.6 reprex_0.3.0      digest_0.6.27    
## [85] webshot_0.5.2     munsell_0.5.0     viridisLite_0.3.0